Finite element approximation of the Dirichlet problem using the boundary penalty method

Numerische Mathematik - This paper considers a finite element approximation of the Dirichlet problem for a second order self-adjoint elliptic equation,Au=f, in a region Ω ⊂ ℝn (n=2...     

Even-aged restrictions with sub-graph adjacency

Restrictions on the size and proximity of clearcuts have led to the development of a variety of exact and heuristic methods to optimize the net present value of timber harvests, subject to adjacency constraints. Most treat harvest units as pre-defined, and impose adjacency constraints on any two units sharing a common border. By using graph theory notation to define sub-graph adjacency constraints, opening size can be considered variable, which may be more appropriate for landscape-level planning. A small example data set is used in this paper to demonstrate the difference between the two types of adjacency constraints for both integer programming and heuristic solution methods.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Bismuth-catalyzed benzylic oxidations with tert-butyl hydroperoxide

[reaction: see text] Oxidation of alkyl and cycloalkyl arenes with tert-butyl hydroperoxide catalyzed by bismuth and picolinic acid in pyridine and acetic acid gave the corresponding benzylic ketones (48-99%). Alternatively, oxidation of methyl arenes gave the corresponding substituted benzoic acids (50-95%). Preliminary mechanistic studies were consistent with a radical mechanism rather than a bismuth(III)-bismuth(V) cycle.     

ROMPgel-supported tris(triphenylphosphine)rhodium(I) chloride: a selective hydrogenation catalyst for parallel synthesis

ROMPgel-supported tris(triphenylphosphine)rhodium(I) chloride has been prepared and the immobilised catalyst has been effectively employed in selective hydrogenations of a variety of alkenes and terminal alkynes.     

Stable sensor layers self-assembled onto surfaces using azobenzene-containing polyelectrolytes.

Polyelectrolytes functionalized with photoisomerizable azobenzene chromophores were multi-layered onto inorganic and metal surfaces, by the repeated adsorption from dilute aqueous solution, alternating between oppositely charged polymers. These layer-by-layer ionically self-assembled thin films were investigated for their suitability as sensor host materials with respect to the criteria of control over physical layer properties, versatility to different substrates and adsorption geometries, and stability of the formed layers to heat, solvent, and sonication. Layer thickness was found to be controllable between 5 A and 500 nm by varying the total number of layers deposited, from a single monolayer to 1000 layers. Control over individual layer thickness was achieved by varying the pH of the adsorption solutions. This multi-layer self-assembly was demonstrated to be suitable for a wide range of metal and inorganic substrates, and achievable with surfaces of high curvature (r = 50 nm), and confined geometry. The deposited layers exhibited good stability to desorption in a range of organic solvents, aqueous temperatures to 100 degrees C, and cleaning protocols such as sonication. The laser-induced geometric isomerization of the azobenzene chromophores was shown to be strongly dependent on aqueous solution properties, demonstrating an application as a hydroxide ion sensor in highly alkaline media.     

Retention behaviour of an homologous series of oligodeoxythymidilic acids using reversed-phase ion-pair chromatography

Summary The retention behaviour of an homologous series of phosphorylated oligodeoxythymidylic acid (pd(T)_5–18) oligonucleotides was studied using reversed-phase ion-pair chromatography with isocratic elution conditions. The effects of temperature, pH, eluent ionic strength, percentage organic modifier, concentration and alkyl chain length of the ion-pairing reagent were investigated. The retention behaviour was generally explicable by current theoretical models of ion-pair chromatography. However, the marked effect of mobile phase pH on the retention of the oligonucleotides was unexpected, and this was ascribed to the presence of ionisable residual silanols on the surface of the reversed-phase packing material.